She had realized that she was no good at being a mother and that Roy was not a good father either, but that did not mean that she should get rid of her daughter, so even if it cost her her life, she continued to take care of her.
There were times, even if she wanted to take care of (or rather, try to take care of) her daughter, she couldn't. she couldn't be a villain and a mother at the same time. In those situations she made the excuse that it was Roy who had to take care of Lian but that excuse reached its limit, she couldn't use it anymore.
She had to look for new solutions, any solution where her daughter would be safe. She actually had no idea who to look for, not friends who wouldn't get into trouble, so she started thinking about some kind of hero she had ever seen with a child. Batman wasn't an option, you were.
So even with little Lian in her arms, she explained everything to you, without letting you refuse the idea of taking care of her daughter. "And please don't let Roy know about this, okay? I'm supposed to stay with Lian but I can't let her get hurt."
She handed you Lian, placing her in your arms